The world-wide growth of spectrally efficient communications systems and the enhancement of their performance has increased the number of individual users and data transmission rates for these systems. Packet-based communication systems whose physical layers are based on multicarrier modulation are commonly referred to as OFDM (Orthogonal Frequency Division Multiplexing) or DMT (Discrete MultiTone) systems. The available transmission channel bandwidth within an OFDM system is subdivided into a number of discrete sub-channels or carriers. Even though these sub-channels overlap, they are orthogonal to each other. Data is transmitted in the form of symbols that have a predetermined duration and encompass some number of carrier frequencies. Systems in compliance with IEEE 802.11a and 802.11g wireless LAN standards are well-known examples of such systems.
The conventional structure of packets in a packet-based data transmission system comprises a preamble, a signal and a data field. The preamble serves to provide boundary detection, channel estimation, carrier recovery. In addition, the preamble serves to initialize the algorithms in the receiver to process the signal and extract the information. The signal field mainly describes the rate of the data and the number of OFDM symbols that follow. Finally, the data field contains the actual OFDM symbols carrying the useful information.
The preamble includes a short and long sequence field, each serving a specific purpose. The short sequence consists of an OFDM symbol repeated two and a half times is used for signal detection, automatic gain control (AGC) setting, coarse frequency offset, and timing synchronization. The long sequence consists also of an OFDM symbol differing from the one in the short sequence. It is repeated two and a half times and is used for channel and fine frequency-offset estimation. Both the long and short sequences have the same duration of 8 μs.
The long sequence X of the preamble is used to estimate the channel frequency response. More particularly, long sequence X is used to estimate the channel where the channel estimation equals:Ĥ=F(FH{tilde over (D)}H{tilde over (D)}F)−1FH{tilde over (D)}V.   [1]Vector V is the Discrete Fourier Transform (DFT) of the convolution of the discrete time channel impulse response h[n] and the discrete time signal sequence u[n]. Matrix {tilde over (D)} is a N×N diagonal matrix, whose diagonal equals the long sequence X. Matrix {tilde over (D)}H is the Hermitian of matrix {tilde over (D)}, wherein Hermitian is the conjugate transpose. Matrix FH is the Hermitian of Discrete Fourier Transform (DFT) matrix F.
Long sequence X is known in advance and is transmitted to probe for the channel. Thus, matrix {tilde over (D)} is known in advance. Matrix Q equals:Q=F(FH{tilde over (D)}H{tilde over (D)}F)−1FH{tilde over (d)}  [2]Matrix R is a real, Toeplitz and symmetric L×L matrix that equals:R=FHDH{tilde over (D)}F   [3]using matrix R, matrix Q reduces to:Q=FR−1FH {tilde over (D)}.   [4]Matrix R−1 is a real and symmetric matrix. In addition, matrix R−1 is symmetric along its antidiagonal from its Southwest element to its Northeast element, and is, therefore, persymmetric. A symmetric matrix that is persymmetric is known as a centrosymmetric matrix. Thus, matrix R−1 is a real and centrosymmetric matrix.
Conventionally, matrix Q is precomputed and stored in a read accessible memory (RAM). Thus, when the observation vector, V, is available, only a matrix vector multiplication is necessary to estimate the channel quality. Unfortunately, matrix Q contains N2 complex numbers. Thus, in systems in compliance with IEEE 802.11a and 802.11g wireless LAN standards where for N=64, four thousand ninety six complex numbers must be stored for a 10 bit word length and, as a result, approximately 10 k bytes of RAM are required. The multiplication of matrix Q with vector V requires N2 complex multiplications which are equivalent to 4N2 real multiplications. As a result, a complexity of 16,384 real multiplications exists.
Thereby, a significant complexity exists using the conventional method. More particularly, the number of the tones that are significant when calculating the channel estimation metric are substantially less than the total number of tones. Thus, there is a need for an alternate way of computing the channel estimation metric that provides a more simple, cost effective approach over that which is conventional.
The present invention is directed to overcoming, or at least reducing the effects of one or more of the problems set forth above.